Allardyce is without a managerial job at the moment, having had his contract at West Ham not renewed at the end of last season.
The former Newcastle United boss rates attacking midfielder Nolan highly and is happy to sign him should he return to management soon.
“Depends on what club I get,” said Allardyce when asked if he would sign Nolan. “He was the catalyst why we started to be successful at West Ham.
“He made the decision to step out of the Premier League at Newcastle and come with me to West Ham who were relegated to the Championship.
“He captained the team brilliantly and took them back up, scored goals. If a club comes along, whatever club it is, if I think that Kevin contribute like he has contributed for me in his career, then that would be yes.”
Good news for West Ham United fans?
Nolan is 33 years of age and is past his prime, and West Ham fans will be happy to know that Allardyce is willing to take him off their books.
The Englishman has been at the Hammers since 2011, but he is likely to struggle for playing time this season.
The former Bolton Wanderers star had a disappointing 2014-15 campaign, scoring just one goal and creating only 12 chances in 29 Premier League appearances.
Nolan’s current contract with West Ham runs out in June 2016, and it would come as a surprise if the Premier League club offered him a new deal.